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This article introduces a multi-step solver for sets of nonlinear equations. To achieve this, we consider and develop a multi-step Steffensen-type method without memory, which does not require evaluations of the Fréchet derivatives, and subsequently extend it to a method with memory. The resulting order is 5 + 2 , utilizing the identical number of functional evaluations as the solver without memory, thereby demonstrating a higher computational index of efficiency. Finally, we illustrate the advantages of the proposed scheme with memory through various test problems. [ABSTRACT FROM AUTHOR]

The present paper examines the temperature-dependent viscosity and thermal conductivity of a micropolar silver ()−Magnesium oxide () hybrid nanofluid made of silver and magnesium oxide over a rotating vertical cone, with the influence of transverse magnetic field and thermal radiation. The physical flow problem has been modeled with coupled partial differential equations. We apply similarity transformations to the non-dimensionalized equations, and the resulting nonlinear differential equations are solved using overlapping grid multidomain spectral quasilinearization method. The flow behavior for the fluid is scrutinized under the impact of diverse physical constraints, which are illustrated graphically. The results of the skin friction coefficient and Nusselt number varying different flow parameters are presented in the form of a table. It is observed that the main flow of the hybrid nanofluid, nano particle fraction of silver and Magnesium/water, enhances compared to the mono-nano fluid as the coupling number increases. The application of studies like this can be found in the atomization process of liquids such as centrifugal pumps, viscometers, rotors, fans. [ABSTRACT FROM AUTHOR]

Nonlinear optimal control problems governed by variable-order fractional integro-differential equations constitute an important subgroup of optimal control problems. This group of problems is often difficult or impossible to solve analytically because of the variable-order fractional derivatives and fractional integrals. In this article, we utilized the expansion of Lagrange polynomials in terms of Chebyshev polynomials and the power series of Chebyshev polynomials to find an approximate solution with high accuracy. Subsequently, by employing collocation points, the problem was transformed into a nonlinear programming problem. In addition, variable-order fractional derivatives in the Caputo sense were represented by a new operational matrix, and an operational matrix represented fractional integrals. As a result, the mentioned integro-differential optimal control problem becomes a nonlinear programming problem that can be easily solved with the repetitive optimization method. In the end, the proposed method is illustrated by numerical examples that demonstrate its efficiency and accuracy. [ABSTRACT FROM AUTHOR]

This study presents an efficient method using the local radial basis function finite difference scheme (RBF-FD). The innovative coefficients are derived from the integrals of the multiquadric (MQ) function. Theoretical convergence rates for the coefficients used in function derivative approximation are provided. The proposed scheme utilizes RBF-FD estimations on three-point non-uniform stencils to construct the final approximation on a tensor grid for the 3D Heston–Hull–White (HHW) PDE, which is relevant in economics and mathematical finance. Numerical evidence and comparative analyses validate the results and the proposed scheme. [ABSTRACT FROM AUTHOR]

We presented some improvements of the inequalities involving the numerical radius powers for products and sums of the operators investigated in the Hilbert space. We generalized and improved numerical radius inequalities with a generalization of the mixed Schwarz inequality. Among other things, with the help of a fraction and its power, as well as the introduction of ξ, we provided a very good improvement for the ωr(E), for E ∈ B(Hs). [ABSTRACT FROM AUTHOR]

This work proposes a new scheme under the umbrella of iteration methods to compute the sign of an invertible matrix. To this target, a review of the exiting solvers of the same type is given and then a new scheme is derived based on a multi-step Newton-type nonlinear equation solver. It is shown that the new method and its reciprocal converge globally with wider convergence radii in contrast to their competitors of the same order from the general Padé schemes. After investigation on the theoretical parts, numerical experiments based on complex matrices of various sizes are furnished to reveal the superiority of the proposed solver in terms of elapsed CPU time. [ABSTRACT FROM AUTHOR]

In this paper, the fractional-order chaotic system form of a four-dimensional system with cross-product nonlinearities is introduced. The stability of the equilibrium points of the system and then the feedback control design to achieve this goal have been analyzed. Furthermore, further dynamical behaviors including, phase portraits, bifurcation diagrams, and the largest Lyapunov exponent are presented. Finally, the global Mittag–Leffler attractive sets (MLASs) and Mittag–Leffler positive invariant sets (MLPISs) of the considered fractional order system are presented. Numerical simulations are provided to show the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Presented in this current study is the numerical analysis of magnetohydrodynamics Williamson nanofluid flow over an exponentially stretching surface. The most important aspect of the investigation is that the effects of the magnetic field, chemical reaction and thermal radiation in the fluid flow are taken into account. The partial differential equations governing the present Williamson nanofluid flow problem were observed to be highly nonlinear and coupled. Suitable similarity transformations were used to transmute the coupled system of nonlinear partial differential equations governing the fluid flow into a linear system. The linear system was solved numerically using the spectral quasi-linearization method. The MATLAB bvp4c numerical technique and a comparison with existing results for the skin friction coefficient were used to confirm the appropriateness of the method in solving the current problem. The influence of some pertinent physical parameters on the fluid's velocity, temperature and concentration profiles were displayed graphically. The effects of all the physical parameters on the skin friction coefficient, Nusselt number and Sherwood number were portrayed in a tabular form. It was noted that enhancing the thermal radiation parameter reduces the fluid's temperature, Nusselt number and the skin friction coefficient, while the Sherwood number is improved. [ABSTRACT FROM AUTHOR]

Investigating the fractal behavior of iteration methods on special polynomials can help to find iterative methods with global convergence for finding special matrix functions. By employing such a methodology, we propose a new solver for the sign of an invertible square matrix. The presented method achieves the fourth rate of convergence by using as few matrix products as possible. Its attraction basin shows larger convergence radii, in contrast to its Padé-type methods of the same order. Computational tests are performed to check the efficacy of the proposed solver. [ABSTRACT FROM AUTHOR]

Here, a new local non-integer derivative is defined and is shown that it coincides to classical derivative when the order of derivative be integer. We call this derivative, adaptive derivative and present some of its important properties. Also, we gain and state Rolle’s theorem and mean-value theorem in the sense of this new derivative. Moreover, we define the optimal control problems governed by differential equations including adaptive derivative and apply the Legendre spectral collocation method to solve this type of problems. Finally, some numerical test problems are presented to clarify the applicability of new defined non-integer derivative with high accuracy. Through these examples, one can see the efficiency of this new non-integer derivative as a tool for modeling real phenomena in different branches of science and engineering that described by differential equations. [ABSTRACT FROM AUTHOR]